Smooth bevel edges using non destructing Boolean
To bevel all sharp edges, you can use the Bevel modifier.

Put Bevel Modifier after the Boolean Modifier and set Limit Method &gt; Angle
To avoid 'tight geometry' that would limit the Bevel, you can create a large N-Gon using the Decimate Modifier (try different delimit methods).
Make sure no tight geometry on your mesh limits the Bevel (in your case there is some)